In the rest of the UK, the opt-in system still applies, although ministers in Scotland and Northern Ireland are likely to be watching what happens in Wales closely.

First Minister Carwyn Jones said it was "law making in Wales at its best".

Ministers have said more than two-thirds of people in Wales are now aware of the changes and they hoped a "leap in consent rates" would follow.

Mr Drakeford said: "There are many, many people who would be prepared to be organ donors but the knowledge of their wishes is not available at the point where this very unusual set of circumstances is significant.

"The law is just one thing we're doing; it will be a profound cultural change.

'Precious gift'

"NHS Blood and Transplant says we need a revolution in consent - we think our law delivers that - and an evolution in practice, and we're part of that UK-wide evolution that will go well beyond 1 December."

He said he was satisfied the balance was right and people had for the very first time the right to register their decision to opt out too.

But the known views of the donor would prevail.

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Media captionSam Scothern had a kidney transplant when he was nine

Mr Drakeford said he welcomed the support of faith groups although there was still some opposition to presumed consent.

The Rt Rev John Davies, Bishop of Swansea and Brecon, said the churches were fully supportive of the issue of organ donation but the preference was to see it as a "gift."

"In the deeming of consent, there is always the risk that that idea of gift might vanish," he said.

"From a Christian or moral perspective, I think the idea of giving someone a precious gift is something much better than others presuming that that gift can be eradicated and just taken."